Yes, the engines were a two cylinder, two cycle if I remember correctly. That meant you mixed oil with gas, like a weedeater. The belched oil smoke.

The bodies were made of a composite of cotton fiber mixed with plastic I think. Sort of a cheap fiberglass. The plastics were known to be long-lasting and rustproof, but I think I've read the plastics were toxic and the bodies do not decay or are in any way recyclable. Environmental disasters, these were.
Wait. Is this the one that's indestructible, or the one that's notoriously unreliable?
I took a tour of Nowa Huta in one of these when I visited Krakow last October. Our driver was a little chain-smoking dude who was also a member of the communist party. The ignition would spark every time he tried to start the car. People in rusted out ford fiestas pointed and laughed. We also had to stop at every service station along the way so he could check what was going on under the hood (something bad, apparently - but his English was about as good as my Polish, so I remained blissfully ignorant). We were told that people would have to enter a lottery for the opportunity to purchase one of these when they were produced; not to win a car, but to be allowed to pay for one next time they came out.

The cars are pretty hilarious (I think the body may be made of plastic) at least to this relatively privileged westerner, but if I had to be reliant on that as daily transpo, I think I would have been eager to escape the Soviet bloc as well!

A couple of pics and the rest of the story here -

Edited at 2011-07-09 03:48 pm (UTC)
Zwickau - I've been there! :D And I've ridden in these - no worse than most tiny cars designed in the 1970s (except it was already 1986 when I rode in one and they hadn't evolved.) The main issue was the 2-stroke (V2) engine, which sounded like a cheap lawnmower - there was a joke about the rich western relatives coming over to East Germany bringing a toy BMW car for the kiddies. The Wessis would explain how powerful the BMW cars were and then the Eastern kids would push them along the carpet going Rrrrnnn-nn-nn-nn-nn (like a windup friction toy). Good times behind the wall.
One of TIME's "50 Worst Cars",28804,1658545_1658533_1658030,00.html

This is the car that gave Communism a bad name. Powered by a two-stroke pollution generator that maxed out at an ear-splitting 18 hp, the Trabant was a hollow lie of a car constructed of recycled worthlessness (actually, the body was made of a fiberglass-like Duroplast, reinforced with recycled fibers like cotton and wood). A virtual antique when it was designed in the 1950s, the Trabant was East Germany's answer to the VW Beetle — a "people's car," as if the people didn't have enough to worry about. Trabants smoked like an Iraqi oil fire, when they ran at all, and often lacked even the most basic of amenities, like brake lights or turn signals. But history has been kind to the Trabi. Thousands of East Germans drove their Trabants over the border when the Wall fell, which made it a kind of automotive liberator. Once across the border, the none-too-sentimental Ostdeutschlanders immediately abandoned their cars. Ich bin Junk!
I like how they put "Luxe" with "Trabant". Seat padding perhaps?